Title: Percolation and Polymerbased Nanocomposites
1Percolation and Polymerbased Nanocomposites
Avik P. Chatterjee Department of Chemistry State
University of New York College of Environmental
Science Forestry
2Outline
 Fiberbased composites percolation the What
and the Why 
 Elastic moduli in rodreinforced
nanocomposites  A unified model that integrates percolation
ideas with effective  medium theory
 Analogy between continuum rod percolation and
site percolation on  a modified Bethe lattice calculation of the
percolation threshold  and percolation and backbone probabilities
 A simple model for systems with nonrandom
spatial  distributions for the fibers
 Future Directions and Acknowledgements
3Composites Percolation
 Composites Mixtures of particles/nanoparticles
(the filler), dispersed  (randomly or otherwise) within another phase
(the matrix)  Basic idea to combine integrate desirable
properties (e.g., low density,  high mechanical moduli or conductivity) from
different classes of material  Natural Composites (e.g. bone and wood) often
exhibit hierarchical  structures, varying organizational motifs on
different scales  Wood for the Trees wood remains one of the
most successful  fiberreinforced composites, and cellulose
the most widelyoccurring  biopolymer (annual global production of wood
1.75 x 109 metric tons)
4Wood A natural, fiberreinforced composite
Cell walls layered cellulose microfibrils
(linear chains of glucose residues, degree of
polymerization ? 5000 10000, ? 4050 w/w of
dry wood depending on species), bound to matrix
of hemicellulose and lignin
R.J. Moon, Nanomaterials in the Forest Products
Industry, McGrawHill Yearbook in Science
Technology, p. 226 229, 2008
5Cellulose Nanocrystals (I)
 Cellulose (linear chains of glucose residues),
bound to matrix of lignin  and hemicellulose, comprises ? 4050 w/w of
dry wood  Individual fibers have major dimensions 13
mm, consisting of spirally  wound layers of microfibrils bound to
ligninhemicellulose matrix  microfibrils contain crystalline domains of
parallel cellulose chains  individual crystalline domains 520 nm in
diameter, 12 ?m in length  Nanocrystalline domains separable from amorphous
regions by  controlled acid hydrolysis (amorphous regions
degrade more rapidly)  Crystalline domain elastic modulus
(longitudinal) 150 GPa compare  martensitic steel 200 GPa, carbon nanotubes
103 GPa  Suggests possible role for cellulose
nanocrystals as a renewable, bio  based, lowdensity, reinforcing filler for
polymerbased nanocomposites
6Cellulose Nanocrystals (II)
 Cellulose microfibrils secreted by certain
nonphotosynthetic bacteria  (e.g. Acetobacter xylinum), and form the
mantle of seasquirts  (tunicates) (e.g. Ciona intestinalis)
 These highly pure forms are free from
lignin/hemicelluloses fermentation  of glucose a possible microbial route to
largescale cellulose production.
Nanocrystalline cellulose whiskers, from acid
hydrolysis of bacterial cellulose. Image courtesy
of Profs. W.T. Winter and M. Roman, Dept. of
Chemistry, SUNYESF, and Dept. of Wood Science
and Forest Products at Virginia Tech.
Adult seasquirts
7Connectedness Percolation What ?
Percolation The formation of infinite, spanning
clusters of connected (defined by spatial
proximity) particles.
Below percolation threshold
Above percolation threshold
8Percolation Why? Dramatic Effects on Material
Properties
Impact Toughness
Z. Bartczak, et al., Polymer, 40, 2331, (1999)
Izod impact energy (J/m)
Average ligament thickness (mm)
t Matrix ligament thickness
Toughness of HDPE/Rubber Composites Rubber
particle size range 0.36 0.87 mm
9Electrical conductivity and Elastic Modulus (I)
 Polypyrrolecoated cellulose whiskers
investigated as electrically  conducting filler particles (L. Flandin, et
al., Compos. Sci. Technol., 61, 895,  (2001) Mean aspect ratio ? 15)
 Mechanical reinforcement/modulus enhancement
(tunicate cellulose  whiskers in poly(ScoBuA), V. Favier et
al., Macromolecules, 28, 6365, (1995)  Mean aspect ratio ? 70)
10Electrical conductivity and Elastic Modulus (II)
 Polystyrene (PS) reinforced with MultiWalled
Carbon Nanotubes  (MWCNTs) (Diameters 150 200 nm Lengths
5 10 ?m T 190o C  critical volume fraction ? 0.019 A.K. Kota,
et al., Macromolecules, 40, 7400, (2007))
11Percolation Thresholds for Rodlike Particles
Percolation threshold for rods, ? ? (D / L),
depends approximately inversely upon aspect
ratio, a result supported by (i) Integral
equation approaches based upon the Connectedness
Ornstein Zernike equation (X. Wang,
A.P. Chatterjee, J. Chem. Phys., 118, 10787,
(2003) R.H.J. Otten and P. van der
Schoot, Phys. Rev. Lett. 103, 225704, (2009))
(ii) MonteCarlo simulations of both
finitediameter as well as
interpenetrable rods (L. Berhan, A.M. Sastry,
Phys. Rev. E, 75, 041120, (2007) M.
Foygel, et al., Phys. Rev. B, 71, 104201,
(2005)) (iii) Excluded volume arguments
(I. Balberg, et al., Phys. Rev. B 30, 39333943,
(1984))
12Elasticity Stress, Strain, Stiffness
 Stress tensor ? (Energy/Volume)
 Strain tensor ? (Dimensionless)
 Stiffness tensor C (Energy/Volume) Fourth
rank tensor  C can have a maximum of 21 independent
elements/elastic coefficients  For an isotropic system, there are only TWO
independent elastic  constants, usually chosen from amongst E,
G, K, ? (tensile, shear,  and bulk modulus, and Poisson ratio,
respectively)  In terms of deformation energy per unit volume,
U  and
, where
13A Seismic Interlude
 Seismic (earthquakegenerated) waves
 Primary/Pressure (Pwaves)
 Longitudinal
 ? 57 km/s in crust, ? 8 km/s in mantle
 Secondary/Shear (Swaves)
 Transverse
 ? 34 km/s in crust, ? 5 km/s in mantle
 Cannot traverse liquid outer core of the
earth  Shadow zones and travel times reveal
information regarding  internal structure of the earth
(Courtesy US Geological Survey)
14Elastic Moduli of Composite Materials
 Simple estimates employing only (i) the volume
fractions ?n, and (ii) the  elastic coefficients En, of the individual
constituents, include the Voigt  Reuss and HashinShtrikman bounds (for
isotropic materials) (Z. Hashin, S.  Shtrikman, J. Mech. Phys. Solids, 11, 127,
(1963))  Arithmetic mean (Hill average) of such bounds
frequently employed as a  semiempirical tool (R. Hill, Proc. Phys. Soc.
London A, 65, 349, (1952) S. Ji, et al., J.  Struct. Geol., 26, 1377, (2004))
Voigt / Parallel
Reuss / Series
15Percolation and Elastic Moduli
 Cellulose nanocrystals modeled as
 circular cylinders, uniform radius R,
 variable lengths L
 Nanocrystals modeled as being
 transversely isotropic, with five independent
 elastic constants Eax, Etr, Gtr, ?ax, ?tr
 Eax 130 GPa, Etr 15 GPa, Gtr 5 GPa, ?ax
?tr 0.3  (L. Chazeau, et al., J. Appl. Polym. Sci., 71,
1797, (1999))  Actual unit cell symmetry monoclinic, implying
13 independent elastic  constants (K. Tashiro, M. Kobayashi, Polymer,
32, 1516, (1991))  Objective To unify percolation ideas with
effective medium theory towards  an integrated model for
composite properties
2 R
L
16Model for Network Contribution to Elasticity
 For network element of length L and radius R
elastic deformation energy U is  Combines stretching, bending, shearing energies,
?ij are  strain components in fiberfixed frame, with
fiber axis in the  Zdirection (F. Pampaloni, et al., Proc. Natl.
Acad. Sci. US., 103,  10248, (2006))
 Assume (i) isotropic orientational
distribution,  (ii) random contacts between rods, Poisson
distribution for lengths of network  elements, and (iii) affine deformation
 Energy of elastic deformation averaged over rod
and segment lengths and  orientations, strain tensor transformed to
laboratory frame, then differentiated twice  with respect to ?ij to obtain estimates
for the network moduli Enet, Gnet  BUT Rods of different lengths will differ in
likelihood of belonging to network, and  for small enough volume fractions, no
network exists !
17Percolation Probability and Threshold
 Percolation probability, denoted P (?, L)
probability that a randomly  selected rod of length L belongs to the
percolating network/infinite cluster  Modeled as
for , and zero otherwise  , Ldependent
percolation threshold  Parameters are treated as
adjustable control transition width  location of threshold
 These assumptions, together with
piecewiselinear (unimodal) model for  the overall distribution over rod lengths L,
allows estimation of  (i) volume fraction of rods belonging to
network (?net),  (ii) volume fraction and length distribution
of rods that remain dispersed,  (iii) average length of network elements
(assuming random contacts)  There remains the task of combining the network
moduli with contributions  from the matrix, and from the dispersed rods
18Moduli for the Composite
 Identify a continuum surrogate for network,
using Swiss cheese analogy, where  (matrix dispersed rods) ? (spherical voids)
 Use MoriTanaka (MT) model to estimate moduli
for an isotropic system made up of  (matrix dispersed rods) (Dispersed rods
treated as lengthpolydisperse, within a discrete
 twocomponent description) (Y.P. Qiu, G.J.
Weng, Int. J. Eng. Sci., 28, 1121, (1990))  Final step again use MoriTanaka (MT) method to
estimate moduli for the system  (continuum network surrogate) (spherical
voids now filled with isotropic system of  matrix dispersed rods, with moduli
determined in previous step)  Recursive use of MT model equivalent in this
context to HashinShtrikman upper  bound
19Results (I)
 Matrix Copolymer of ethylene oxide
epichlorohydrin (EOEPI)  Filler Tunicate cellulose whiskers (solution
cast system)  Mean whisker radius R 13.35 nm
 Whisker Lengths Ln 2.23 ? m, Lmax 5.37 ? m
(reproduces first two  moments of experimentally measured
distribution)  Solid Line Polydispersity in rod lengths
included in model  Broken Line Model treats rods as monodisperse,
J.R. Capadona, et al., Nat. Nanotechnol., 2, 765,
(2007) D.A. Prokhorova, A.P. Chatterjee,
Biomacromolecules, 10, 3259, (2009)
20Results (II)
 Matrix waterborne polyurethane (WPU)
 Filler Flax cellulose nanocrystals
 Mean whisker radius R 10.5 nm
 Whisker Lengths Ln 327 nm, Lmax 500 nm
(based on experimentally  measured distribution of rod lengths)
 Solid Line Polydispersity in rod lengths
included in model  Broken Line Model treats rods as monodisperse,
X. Cao, et al., Biomacromolecules, 8, 899,
(2007) D.A. Prokhorova, A.P. Chatterjee,
Biomacromolecules, 10, 3259, (2009)
21Results (III)
 Matrix Copolymer of styrene butyl acrylate
(poly(ScoBuA))  Filler Tunicate cellulose whiskers
 Mean whisker radius R 7.5 nm
 Whisker Lengths Ln 1.17 ? m, Lmax 3.0 ? m
(based on experimentally  measured distribution of rod lengths)
 Solid Line Polydispersity in rod lengths
included in model  Broken Line Model treats rods as monodisperse,
M.A.S.A. Samir, F. Alloin, A. Dufresne,
Biomacromolecules, 6, 612, (2005) D.A.
Prokhorova, A.P. Chatterjee, Biomacromolecules,
10, 3259, (2009)
22Can Continuum Rod Percolation be related to
Percolation on the Bethe Lattice ?
 Perfect dendrimer/Cayley tree, with uniform
 degree of branching z at each vertex
 No loops/closed paths available
 Extensively studied as exemplar of
 meanfield lattice percolation
 (M.E. Fisher, J.W. Essam, J. Math. Phys., 2,
609,  (1961) R.G. Larson, H.T. Davis, J. Phys. C,
15, 2327,  (1982))
 If vertices are occupied with probability
 ?, then site percolation threshold located
 at ? (1/(z 1))
Portion of a Bethe lattice with z 3
 Given how thoroughly this problem has been
examined,question  arises whether one can relate continuum rod
percolation to  percolation on the Bethe lattice
23Continuum Rod Percolation ? Bethe Lattice A
simpleminded mapping
 Consider a population of rods, with uniform
radius R, but variable lengths  L. We let denote the distribution
over rod lengths  On average a rod of length L experiences ? ?
(L/R) contacts with other rods  in the system
 For a Bethe lattice with degree z each occupied
site has (on average) z ?  contacts with nearest neighbor occupied
sites  Suggests the following analogy
 Rod ? Occupied lattice site
 ? ?
?  z ? z (L) ? (L/R)
The corresponding Bethe lattice must have a
distribution of vertex degrees
24Percolation on a modified Bethe Lattice
 Bethe Lattice Analog Site percolation on a
 modified Bethe lattice, with site occupation
 probability ? , and with vertex degree
 distribution f (z) that can be obtained from
 the underlying rod length distribution
 Let Probability that a randomly chosen
 branch in such a lattice, for which it is
known  that one of the terminal sites is occupied,
 does not lead to the infinite cluster
 Given the absence of closed loops, is
 determined by (M.E.J. Newman, et al., Phys.
Rev.  E, 64, 026118, (2001) M.E.J. Newman, Phys.
Rev.  Lett., 103, 058701, (2009))
Illustration of a portion of modified Bethe
lattice
where the summation runs over all values of z
(L), and depends only upon ? and f (z)
25Percolation Threshold and Probability
 Percolation probability for a rod of length L
probability that an occupied  site with vertex degree z (L) belongs to the
infinite cluster 
 Percolation threshold value of ? at which a
solution exists for other  than the trivial solution 1, P 0
 for the case that L gtgt R for all rods in the
system (A.P. Chatterjee, J. Chem.  Phys., 132, 224905, (2010) an identical
result was derived in the field of scale free  (power law) networks some years ago, R.
Albert, A.L. Barabasi, Rev. Mod. Phys., 74, 47,  (2002))
 Percolation threshold governed by
weightaveraged aspect ratio  consistent with results from a recent integral
equationbased study (R.H.J.  Otten, P. van der Schoot, Phys. Rev. Lett.,
103, 225704, (2009))
26Generalization to finitediameter rods
 Model rods as hard core soft shell
 entities hard core radii and lengths
 denoted R, L, and soft shell radii and
 lengths given by R l, L 2 l
 For this problem, an identical approach yields
 (A.P. Chatterjee, J. Statistical Physics, 146,
244, (2012))  This is in full agreement with recent findings
based on integral equation  approach, for arbitrarily correlated joint
distributions over rod radii and  lengths (R.H.J. Otten, P. van der Schoot,
Phys. Rev. Lett. 103, 225704, (2009), J.  Chem. Phys. 134, 094902, (2011))
 Result can be generalized to particles with
arbitrary crosssectional  shapes, not just circular cylinders (A.P.
Chatterjee, J. Chem. Phys., 137,  134903, (2012))
27Network and Backbone Volume Fractions
 A particle is said to belong to the backbone
of the network if it  experiences at least two contacts with the
infinite cluster  Let B (z (L)) Probability that a rod of length
L belongs to the backbone  Then
(R.G. Larson, H.T. Davis, J.
Phys. C,  15, 2327, (1982))
 Volume fractions occupied by the network, and
network backbone  Near Threshold
 where Lw , Lz are weight and zaveraged rod
lengths, respectively  (A.P. Chatterjee, J. Chem. Phys., 132,
224905, (2010))
28Illustrative Results for Percolation Backbone
Probabilities
 Polydisperse Rods Unimodal Beta distribution,
with Lmin 8.33 R,  Lmax 800 R, Ln 66.67 R, Lw 100 R 1.5
Ln, Lz 133.34 R 2 Ln  ? Black curves
 Monodisperse Rods (for comparison) Ln Lw Lz
100 R, same  percolation threshold as the polydisperse rod
population  ? Red curves
Upper Black Curves L Lmax Lower Black Curves
L Lmin
29Network Backbone Volume Fractions
 Polydisperse Rods Unimodal Beta distribution,
with Lmin 8.33 R,  Lmax 800 R, Ln 66.67 R, Lw 100 R 1.5
Ln, Lz 133.34 R 2 Ln  ? Black curves
 Monodisperse Rods (for comparison) Ln Lw Lz
100 R, same  percolation threshold as the polydisperse rod
population  ? Red curves
Network, backbone, volume fractions lower for
polydisperse system
30Comparison with Monte Carlo Simulations
 Monte Carlo (MC) simulations
 for various polydisperse
 rod systems (B. Nigro et al.,
 Phys. Rev. Lett., 110, 015701, (2013))
 MC results show reasonable agreement
 with theory
 p Number fraction of long rods
 for bidisperse systems
 Symbols MC results, various
 values of p and distributions
 of aspect ratios
 Solid Line Theory based upon modified Bethe
lattice
31Average number of Contacts at Threshold
 Average number of contacts
 per particle at threshold
 where z is the vertex degree
 in the modified Bethe lattice
 For polydisperse systems,
 Nc can be smaller than unity
 MC results show qualitative
 agreement with this result
 (B. Nigro et al., Phys. Rev. Lett.,
 110, 015701, (2013))
 p Number fraction of long rods,
 bidisperse systems
A similar result (Nc lt 1) has been reported for
hyperspheres in highdimensional spaces (N.
Wagner, I. Balberg, and D. Klein, Phys. Rev. E
74, 011127, (2006))
32Nonrandom Spatial Distribution of Particles
Heterogeneity effects
 Foregoing results assume particles are
distributed in a spatially  random, homogeneous fashion
 But particle distribution may in reality
display local clustering or  aggregation, apparent volume fraction may
show statistical non  uniformities/fluctuations
 VERY SIMPLE microstructural descriptors that
capture such  mesoscale heterogeneity
 (i) Pore radius distribution, and moments
thereof, e.g. mean pore  radius, and
 (ii) Chord length distribution, and mean
chord length in the matrix  phase (S. Torquato, Random Heterogeneous
Materials Microstructure and  Macroscopic Properties (Springer, New
York, 2002))
33Pore Radius Chord Length Distributions (I)
 Mean values for the pore radius (ltr gt) and chord
length (lc) provide  simple and physically transparent means for
quantifying spatial  nonrandomness
 Goal to construct as simple a description as
possible in terms of  such variables, and to use these as vehicles
to examine the impact  of spatial heterogeneity upon elastic moduli
34Pore Radius Chord Length Distributions (II)
 Starting point Random distribution of rods we
start with a generalization  of the traditional Ogston result for the
distribution of pore sizes in a fiber  network, generalized to partially account for
fiber impenetrability  (A.G. Ogston, Trans. Faraday Soc., 54, 1754,
(1958) J.C. Bosma and J.A. Wesselingh, J.  Chromatography B, 743, 169, (2000) A.P.
Chatterjee, J. Appl. Phys., 108, 063513, (2010))  Pore radius distribution in network
 of fibers of radius R, volume
 fraction f
 Mean and meansquared pore radii

where 
35Comparison to Ogston model (D. Rodbard and A.
Chrambach, Proc. Natl. Acad. Sci., 65, 970,
(1970))
 In the traditional Ogston model
 where represents the nominal fiber
volume fraction  Relation between models

 (M.J. Lazzara, D. Blankschtein, W.M. Deen,
 J. Coll. Interfac. Sci., 226, 112, (2000))
 For small enough rod volume fractions
 and our treatment reduces to that of Ogston
when f ltlt 1
36Averaging over Fluctuations in f
 Simplest possible ansatz bimodal distribution
over mesoscale fibre  volume fractions, represent distribution over
f by 

where macroscopic 
fiber volume fraction  This distribution function must be
interpreted in a strictly operational sense !!!  Distribution over pore radii, averaged over
mesoscopic fluctuations in f 
 where is the result for
a  random distribution of fibers
 Mean and meansquared pore radii, and mean chord
lengths, can then  be expressed in terms of


37Simple estimation of moduli as functions of
nonrandomness in f
 Use the foregoing formalism in inverse manner to
determine f1, f2 for  specified values of ltf gt , and for the mean
pore radius and chord length  Values of lt f gt, f1, f2 then used with Hill
average (arithmetic mean) of  the ReussVoigt bounds (R. Hill, Proc. Phys.
Soc. A 65, 349, (1952) J. Dvorkin, et  al., Geophysics 72, 1, (2007)) to estimate
modulus in terms of lt r gt and lt lcgt
Solid Line Modulus for uniform fiber
distribution (supplied as ansatz) Upper and lower
broken lines Hill average of ReussVoigt bounds,
obtained from model when lt r gt and lt lcgt each
exceed their values for a random fiber
distribution by factors of 2 and 3,
respectively (A.P. Chatterjee, J. Phys.
Condensed Matter 23, 155104, (2011))
38Basic Conclusion
 Mesoscale fluctuations in f lead to
 (i) increase in the mean pore radius and chord
length  (ii) reduction in the moduli of the material
(within the empirical ReussVoigtHill  averaging scheme)
 Alteration in the mean pore radius/pore radius
distribution may be  expected to also affect transport properties,
e.g., the diffusion coefficient  for a spherical tracer
 Hindered diffusion model Cylindrical fibers
(radius R) pose steric  obstacles to motion of a spherical tracer
(radius R0), specific interactions  neglected
39Tracer Diffusion in nonrandom fiber networks (I)
 Map the pore size distribution for the
nonrandom fiber network from our  model that for the cylindrical
cell model (B. Jonsson, et al., Colloid  Polym. Sci. 264, 77, (1986) L. Johansson,
et al., Macromolecules 24, 6024, (1991))  Operational volume fraction distribution
function y (f) maps onto  distribution over radii in the cylindrical
cell model
40Tracer Diffusion in nonrandom fiber networks (II)
 For cylindrical cell model diffusion constant,
D, for a spherical tracer of  radius R0 in system of fibers of radius R
satisfies (L. Johansson, et al.,  Macromolecules 24, 6024, (1991))
 where h (a) Distribution over outer radii
in cell model,  and D0 unhindered diffusion constant for
the same tracer when fiber  volume fraction vanishes
 Mapping procedure using bimodal distribution for
y (f)  permits expressing h (a) in terms
of mean pore radius mean  chord length for the fiber
network as a whole
41Qualitative findings
 Results of accounting in this manner for spatial
fluctuations in f  For randomly distributed fibers our approach
leads to a value for D that is  consistently below DOgston , where DOgston
arises from combining Ogston  result for pore radius distribution the
cylindrical cell model  Quite generally Spatial fluctuations in f are
predicted to increase D, so long  as diffusion is controlled primarily by
steric/excludedvolume effects
Figure shows D / DOgston for different ratios of
the tracer radius (R0) to fiber radius (R) for
randomly distributed fibers
E1 Exponential Integral
42Tracer Diffusion Some results (I)
 Diffusion of Bovine Serum Albumin (BSA) (R0
3.6 nm) in  polyacrylamide gel (R 0.65 nm)
 Triangles Experiment (J. Tong and J.L.
Anderson, Biophys. J., 70, 1505, (1996))
Legend 1 Fiber distribution random, steric
effects only 2 Fiber distribution random, steric
as well as hydrodynamic effects included (R.J.
Phillips, Biophys. J., 79, 3350, (2000)) 3
Steric and hydrodynamic factors both included,
but fiber distribution nonrandom Mean pore
radius and chord length are each 1.5 times larger
than for a random fiber network with equal ltf gt
(A.P. Chatterjee, J. Phys. Condensed Matter, 23,
375103, (2011))
43Tracer Diffusion Some results (II)
 Diffusion of Bovine Serum Albumin (BSA) (R0
3.6 nm) in calcium  alginate gels (R 0.36 nm)
 Triangles Experiment (B. Amsden, Polym. Gels
Networks, 6, 13, (1998))
Legend 1 Fiber distribution random, steric
effects only 2 Fiber distribution random, steric
as well as hydrodynamic effects included (R.J.
Phillips, Biophys. J., 79, 3350, (2000)) 3
Steric and hydrodynamic factors both included,
but fiber distribution nonrandom Mean pore
radius and chord length are each 1.5 times larger
than for a random fiber network with equal ltf gt
44 Future Directions
 Modeling frequencydependent moduli, perhaps by
way of  the viscoelastic correspondence principle
 Modeling anisotropic systems, where fibers have
some  degree of orientational ordering
 Generalizations to other particle morphologies,
e.g., disks  and persistent/semiflexible linear particles
 Generalization of the analogy to the Bethe
lattice to  account for local clustering effects (M.E.J.
Newman, Phys. Rev. Lett.,  103, 058701, (2009))
 Unification of Bethelattice based percolation
analyses with  simple descriptions of nonrandom
microstructures
45Acknowledgements
From SUNYESF Dr. Xiaoling Wang Ms. Darya
Prokhorova Dr. DeAnn Barnhart Profs. W.T. Winter
and I. Cabasso From other institutions Prof.
Alain Dufresne Prof. Henri Chanzy Prof. Laurent
Chazeau Prof. Christoph Weder Prof. Jeffrey
Capadona Prof. George Weng Prof. Paul van der
Schoot Prof. Claudio Grimaldi Prof. Isaac
Balberg Dr. Ronald Otten Dr. Biagio Nigro USDA
CSREES National Research Initiative Competitive
Grants Program USDA CSREES McIntireStennis
Program National Science Foundation Research
Foundation of the State University of New York